Kinematics and Dynamics Model via Explicit Direct and Trigonometric Elimination of Kinematic Constraints

  • Moritz SchapplerEmail author
  • Torsten Lilge
  • Sami Haddadin
Conference paper
Part of the Mechanisms and Machine Science book series (Mechan. Machine Science, volume 73)


The efficient implementation of kinematics and dynamics models is a key to model based control of mechatronic systems such as robots and wearable assistive devices. This paper presents an approach for the derivation of these models in symbolic form for constrained systems based on the explicit elimination of the kinematic constraints using substitution variables with trigonometric expressions and the Lagrange equations of the second kind. This represents an alternative solution to using the implicit form of the constraints or using the explicit elimination at comparable computational effort. The method is applied to a novel exoskeleton designed for craftsmen force assistance, which consists of multiple planar closed kinematic loops and gear mechanisms.


dynamics closed-loop Lagrangian equations substitution variables explicit form trigonometric expressions 


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The presented work was funded by the Federal Ministry of Education and Research of Germany (BMBF) under grant number 16SV6175 and has also received funding from European Union’s Horizon 2020 research and innovation programme under grant agreement No. 688857 (“SoftPro”).


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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Moritz Schappler
    • 1
    Email author
  • Torsten Lilge
    • 2
  • Sami Haddadin
    • 3
  1. 1.Institute for Mechatronic Systems, Leibniz University HannoverHannoverGermany
  2. 2.Institute for Automatic Control, Leibniz University HannoverHannoverGermany
  3. 3.Chair of Robotics Science and Systems Intelligence, Technical University of MunichHannoverGermany

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